2.1 Probability & Theoretical Distributions — Test 1

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2.1 Probability & Theoretical Distributions — Test 1

Q1. The probability of any event always lies between:✓ 0 and 1 (inclusive)

Q2. The binomial distribution applies to experiments with:✓ A fixed number of independent trials, each with two outcomes

Q3. For a binomial distribution with n trials and success probability p, the mean is:✓ np

Q4. The variance of a binomial distribution is:✓ npq (where q = 1 − p)

Q5. The Poisson distribution is typically used to model:✓ The number of rare events occurring in a fixed interval

Q6. A special property of the Poisson distribution is that its mean and variance are:✓ Equal (both equal to λ)

Q7. The normal distribution curve is:✓ Bell-shaped and symmetric about the mean

Q8. In a normal distribution, the mean, median and mode are:✓ All equal

Q9. According to the empirical (68–95–99.7) rule, about 95% of values in a normal distribution lie within:✓ 2 standard deviations of the mean

Q10. The standard normal distribution has a mean and standard deviation of:✓ Mean 0 and standard deviation 1

Q11. The total area under any normal distribution curve is equal to:✓ 1

Q12. The binomial and Poisson distributions are both:✓ Discrete distributions

Q13. The Poisson distribution can approximate the binomial when:✓ n is large and p is small

Q14. A single trial with only two possible outcomes (success/failure) is called a:✓ Bernoulli trial

Q15. The normal distribution is a ____ distribution, whereas the binomial is a ____ distribution.✓ Continuous; discrete

Q16. The Z-score of an observation tells us:✓ How many standard deviations it lies from the mean

Q17. As the number of trials n becomes large, the binomial distribution can be approximated by the:✓ Normal distribution

Q18. An event with probability 0 is one that is:✓ Impossible

Q19. The parameter that completely specifies a Poisson distribution is:✓ The mean rate λ

Q20. Match each distribution/term with its property and select the correct option.✓ A-iv, B-ii, C-i, D-iii